A360637 Least crossing number of a prime knot with braid index n.

3, 4, 6, 8, 10, 12

Offset

2,1

Links

Table of n, a(n) for n=2..7.

Example

The trefoil knot 3_1 is the smallest prime knot with braid index 2, so a(2) = 3.
The figure-eight knot 4_1 is the smallest prime knot with braid index 3, so a(3) = 4.
The stevedore's knot 6_1 is the smallest prime knot with braid index 4, so a(4) = 6.
The smallest prime knots with braid index 5 are 8_1, 8_3, and 8_12, so a(5) = 8.
The smallest prime knots with braid index 6 are 10_1, 10_3, 10_13, 10_35, and 10_58, so a(6) = 10.
The smallest prime knots with braid index 7 are 12a_125, 12a_128, 12a_181, 12a_183, 12a_197, 12a_448, 12a_471, 12a_477, 12a_482, 12a_690, 12a_691, 12a_803, 12a_1124, 12a_1127, 12a_1166, 12a_1202, and 12a_1287 so a(7) = 12.

Crossrefs

Cf. A002863.

Sequence in context: A027669 A027696 A027440 * A169866 A029902 A286992

Adjacent sequences: A360634 A360635 A360636 * A360638 A360639 A360640

Keyword

nonn,more

Author

Charles R Greathouse IV, Feb 14 2023

Status

approved